Highest Common Factor of 252, 600, 402, 85 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 252, 600, 402, 85 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 252, 600, 402, 85 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 252, 600, 402, 85 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 252, 600, 402, 85 is 1.
HCF(252, 600, 402, 85) = 1
HCF of 252, 600, 402, 85 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 252, 600, 402, 85 is 1.
Highest Common Factor of 252,600,402,85 is 1
Step 1: Since 600 > 252, we apply the division lemma to 600 and 252, to get
600 = 252 x 2 + 96
Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 96 and 252, to get
252 = 96 x 2 + 60
Step 3: We consider the new divisor 96 and the new remainder 60, and apply the division lemma to get
96 = 60 x 1 + 36
We consider the new divisor 60 and the new remainder 36,and apply the division lemma to get
60 = 36 x 1 + 24
We consider the new divisor 36 and the new remainder 24,and apply the division lemma to get
36 = 24 x 1 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 252 and 600 is 12
Notice that 12 = HCF(24,12) = HCF(36,24) = HCF(60,36) = HCF(96,60) = HCF(252,96) = HCF(600,252) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 402 > 12, we apply the division lemma to 402 and 12, to get
402 = 12 x 33 + 6
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 6 and 12, to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 12 and 402 is 6
Notice that 6 = HCF(12,6) = HCF(402,12) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 85 > 6, we apply the division lemma to 85 and 6, to get
85 = 6 x 14 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 85 is 1
Notice that 1 = HCF(6,1) = HCF(85,6) .
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Frequently Asked Questions on HCF of 252, 600, 402, 85 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 252, 600, 402, 85?
Answer: HCF of 252, 600, 402, 85 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 252, 600, 402, 85 using Euclid's Algorithm?
Answer: For arbitrary numbers 252, 600, 402, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
